Simplify the following expression: $ t = \dfrac{-1}{q + 9} - \dfrac{4}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-1}{q + 9} \times \dfrac{7}{7} = \dfrac{-7}{7q + 63} $ Multiply the second expression by $\dfrac{q + 9}{q + 9}$ $ \dfrac{4}{7} \times \dfrac{q + 9}{q + 9} = \dfrac{4q + 36}{7q + 63} $ Therefore $ t = \dfrac{-7}{7q + 63} - \dfrac{4q + 36}{7q + 63} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{-7 - (4q + 36) }{7q + 63} $ Distribute the negative sign: $t = \dfrac{-7 - 4q - 36}{7q + 63}$ $t = \dfrac{-4q - 43}{7q + 63}$